Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.4s (42.9%)

Results

1.3s	2076×	body	1024	valid
587.0ms	4614×	body	128	valid
347.0ms	1070×	body	512	valid
110.0ms	491×	body	256	valid
5.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series22.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

14.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
8.0ms	(*.f64 z (cos.f64 y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(*.f64 z (cos.f64 y))
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-rgt-neg-in_binary64`
557×	`distribute-lft-neg-in_binary64`
467×	`fma-neg_binary64`
332×	`*-commutative_binary64`
297×	`neg-mul-1_binary64`

Counts

90 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	960
1	173	908
2	526	895
3	1471	895
4	3145	895
5	4780	895
6	4991	895
7	4926	895

prune47.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	8	65

Error

0.0b

Counts

65 → 8

Alt Table

Status	Error	Program
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	36.5b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	36.2b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
▶	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	17.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	32.2b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 1144 to 401 computations (64.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	0.1b	(*.f64 (sin.f64 y) x)

series24.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

16.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
8.0ms	(*.f64 (sin.f64 y) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (sin.f64 y) x)
0.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
405×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
293×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	852
1	184	793
2	507	781
3	1282	780
4	2630	780
5	4874	780
6	4926	780

prune63.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	64	10	74

Error

0.0b

Counts

74 → 10

Alt Table

Status	Error	Program
	36.2b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
	44.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x))))
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	32.2b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	26.9b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	22.9b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	17.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 1239 to 455 computations (63.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series1.1s (20.2%)

Counts

4 → 72

Calls

4 calls:

686.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
235.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
174.0ms	(cbrt.f64 (cos.f64 y))
20.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
7.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
2.0ms	(cbrt.f64 (cos.f64 y))

simplify163.0ms (3%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
609×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
370×	`cancel-sign-sub-inv_binary64`
351×	`log-prod_binary64`

Counts

174 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	2118
1	352	1762
2	1218	1642
3	2345	1606
4	4484	1588
5	4900	1588
6	4962	1588

prune288.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	219	11	230

Error

0.0b

Counts

230 → 11

Alt Table

Status	Error	Program
	36.2b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
	44.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	32.2b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	26.9b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	22.9b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	17.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 5165 to 1589 computations (69.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

series311.0ms (5.6%)

Counts

3 → 40

Calls

3 calls:

298.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
8.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
5.0ms	(pow.f64 (cos.f64 y) 2)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 61

Calls

3 calls:

8.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify129.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

667×	`unswap-sqr_binary64`
626×	`fma-def_binary64`
343×	`fma-neg_binary64`
324×	`exp-prod_binary64`
322×	`log-prod_binary64`

Counts

101 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1345
1	282	1135
2	923	1093
3	1865	1081
4	4189	1081
5	4716	1081
6	4899	1081

prune179.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	126	11	137

Error

0.0b

Counts

137 → 11

Alt Table

Status	Error	Program
	36.2b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
	44.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x))))
✓	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	32.2b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	26.9b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	22.9b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	17.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 2788 to 1350 computations (51.6% saved)

regimes321.0ms (5.8%)

Accuracy

Total 0.1b remaining (64.3%)

Threshold costs 0.1b (64.3%)

Counts

74 → 1

Compiler

Compiled 4580 to 2726 computations (40.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	14	12
2	13	12

end156.0ms (2.8%)

Compiler: Compiled 231 to 125 computations (45.9% saved)

Details

analyze2.0ms (0%)

sample2.4s (42.9%)

simplify43.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series22.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify105.0ms (1.9%)

prune47.0ms (0.9%)

localize7.0ms (0.1%)

series24.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify81.0ms (1.5%)

prune63.0ms (1.1%)

localize10.0ms (0.2%)

series1.1s (20.2%)

rewrite28.0ms (0.5%)

simplify163.0ms (3%)

prune288.0ms (5.2%)

localize16.0ms (0.3%)

series311.0ms (5.6%)

rewrite14.0ms (0.3%)

simplify129.0ms (2.3%)

prune179.0ms (3.2%)

regimes321.0ms (5.8%)

simplify2.0ms (0%)

end156.0ms (2.8%)

Profiling